The present invention relates to an image processing apparatus and a refractive index distribution measuring apparatus for providing an internal refractive index distribution of an object such as an optical element, and more particularly, to an apparatus for providing an internal refractive index distribution by analyzing a transmitted wavefront or interference fringes.
In recent years, optical elements such as lenses for use in digital cameras and laser-beam printers are often manufactured by molding of optical glass or plastic, and also, optical element shaving aspheric surfaces or free-form surfaces are often manufactured by molding. The molding enables processing of aspheric surfaces at low cost, but produces a nonuniform refractive index distribution within an optical element resulting from a molding time or a molding pressure in manufacture. The presence of the nonuniform refractive index distribution significantly affects the image-forming ability and the like of the optical element which requires high optical performance, so that design values cannot be achieved. Based on that fact, the measurement of the refractive index distribution is an important issue and high-accuracy measurement is needed.
In general, the measurement of a transmitted wavefront with an interferometer is widely used as a method of measuring a refractive index distribution. In conventional methods, however, only a refractive index distribution obtained from integration in a transmission direction of light is observed, and a three-dimensional refractive index distribution such as an internal distribution cannot be provided. To determine the three-dimensional distribution, an optical element to be tested must be measured in several parts, for example by slicing it, and high-accuracy measurement is difficult to achieve.
To solve the problem, Japanese Patent No. 3423486 has disclosed a method in which an object under test is immersed in matching oil having substantially the same refractive index as that of the object under test, and while the object under test is rotated around an axis orthogonal to the optical axis of a wave for test, transmitted wavefronts are measured successively, and an internal distribution is estimated in the cross section of the wave for test from the images of the transmitted wavefronts by performing CT (Computerized Tomography) analysis.
However, the change from interference fringes to transmitted wavefronts involves problems such as an error in a dense part of the interference fringes and a phase jump, and thus accurate transmitted wavefronts cannot be provided in many cases. Particularly, since the CT analysis used in the method disclosed in Japanese Patent No. 3423486 described above utilizes the Fourier transform, it cannot be performed if the images of transmitted wavefronts have any loss due to the abovementioned problems, an opaque part of the object under test, and the like. In addition, the measurement direction of the transmitted wavefronts is limited to one orthogonal to the axis around the single axis, so that it is difficult to provide a stable and accurate refractive index distribution.
Furthermore, in the wavefronts changed from the interference fringes, each pixel has a different expected error amount, but the difference in the error amount for each pixel cannot be reflected in the estimation of the refractive index distribution, leading to a reduction in accuracy.